Advertisements
Advertisements
Question
The length of the diagonals of a rhombus is in ratio 4 : 3. If its area is 384 cm2, find its side.
Advertisements
Solution
Let the lengths of the diagonals of a rhombus are 4x, 3x.
∴ Area of the rhombus = `1/2 xx ("Product of its diagonals")`
= `1/2 (4x xx 3x) = 384` (given)
⇒ `6x^2 = 384 ⇒ x^2 = 64`
⇒ x = 8 cm
∴ Diagonals are `4 xx 8 = 32` cm and `3(8) = 24` cm.
∴ OC = 16 cm and OD = 12 cm
∴ Side DC = `sqrt("OC"^2 + "OD"^2)`
∴ Side DC = `sqrt(16^2 + 12^2)` [By Pythagoras Theorem in ΔDOC]
= `sqrt(256 + 144) = sqrt(400) = 20` cm
Hence , side of the rhombus = 20 cm.
APPEARS IN
RELATED QUESTIONS
Lengths of the diagonals of a rhombus are 16.5 cm and 14.2 cm, find its area.
The area of a rhombus is equal to the area of a triangle. If the base ∆ is 24 cm, its corresponding altitude is 16 cm and one of the diagonals of the rhombus is 19.2 cm. Find its other diagonal.
Find the area of a rhombus whose diagonals are of lengths 10 cm and 8.2 cm.
Find the area of rhombus PQRS shown in the following figure.
Find the area of rhombus PQRS shown in the following figure.
Find the area of a rhombus whose base is 14 cm and height is 9 cm.
Find the missing value.
| Diagonal (d1) | Diagonal (d2) | Area |
| 26 m | 468 sq.m |
What is the area of the rhombus ABCD below if AC = 6 cm and BE = 4 cm?
The area of a rectangular field is 48 m2 and one of its sides is 6 m. How long will a lady take to cross the field diagonally at the rate of 20 m/minute?
Most of the sailboats have two sails, the jib and the mainsail. Assume that the sails are triangles. Find the total area sail of the sailboats to the nearest tenth.
